Adaptive stabilization of nonnecessarily inversely stable first-order continuous-time systems under saturated input (Q1866128)

This paper presents an adaptive stabilization algorithm for first-order continuous-time systems with a zero which can be either stable or unstable under saturated input. The saturating device is modelled by a sigmoidal function. The adaptive scheme uses a parameter modification rule which guarantees that the absolute value of the determinant of the Sylvester matrix associated with the modified parameter estimates is bounded from below by a positive threshold and, thus, the estimated model is guaranteed to be controllable. The modification mechanism involves the use of a hysteresis switching function. An alternative hybrid scheme, whose estimated parameters are updated at sampling instants, is also given to solve a similar adaptive stabilization problem. Convergence and stability results are obtained with use of Lyapunov functions method.